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Single-Particle Analysis

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Cryo-EMDiffraction and Fourier Transforms→→Macromolecular Assemblies
single-particle image-processing 2D-classification 3D-reconstruction RELION cryoSPARC

Core Idea

Single-particle analysis is the computational pipeline that converts thousands to millions of noisy 2D cryo-EM images of individual molecules into a high-resolution 3D density map. The process involves particle picking (identifying and extracting individual molecule images from micrographs), 2D classification (grouping similar views and removing junk), 3D reconstruction (determining the orientation of each particle and combining them into a 3D map), and refinement (iteratively improving the orientation assignments and map quality). Modern software (RELION, cryoSPARC) uses maximum-likelihood statistical frameworks and GPU-accelerated computation. A key capability is 3D classification, which can separate conformationally heterogeneous particles into distinct classes, revealing multiple functional states from a single specimen.

Explainer

A single cryo-EM micrograph contains thousands of individual protein molecules, each frozen in a random orientation, embedded in noisy vitreous ice. Each particle image is a 2D projection of the 3D molecule viewed from whatever angle the particle happened to be at when it was frozen. The challenge of single-particle analysis is to take these millions of noisy, randomly oriented 2D snapshots and reconstruct the 3D structure of the molecule.

The pipeline begins with particle picking — automated algorithms (often using neural networks trained on manually selected examples) scan micrographs and identify locations where individual protein particles are located, extracting small image windows centered on each particle. Next, 2D classification groups particles with similar views, aligns them, and averages within each class. This serves two purposes: it verifies particle quality (classes should show recognizable molecular features) and removes junk (ice contamination, aggregates, denatured particles that do not classify into sensible averages).

The core of the reconstruction is orientation determination — figuring out the three Euler angles (the viewing direction) for each particle. Early methods used common-lines algorithms (each pair of 2D projections of the same 3D object shares a common one-dimensional line). Modern methods use maximum-likelihood approaches (implemented in RELION and cryoSPARC) that do not assign a single orientation to each particle but instead compute the probability of each particle having each possible orientation, weighting contributions accordingly. This probabilistic approach is more robust to noise. Once orientations are assigned, particles are combined into a 3D reconstruction using Fourier inversion — essentially filling in a 3D Fourier volume with the 2D Fourier transforms of each particle at their determined orientations, then inverting to real-space density.

3D classification extends the method to heterogeneous samples. If the molecule exists in multiple conformational states, forcing all particles into a single 3D reconstruction produces a blurred average. Classification algorithms assign each particle to one of K conformational classes (K is specified by the user or determined automatically), producing separate 3D maps for each class. This capability is uniquely powerful — it reveals the structural basis of functional dynamics from a single frozen sample. A ribosome dataset might yield separate maps for initiation, elongation, and termination states; a membrane channel might show open, closed, and desensitized conformations. Combined with time-resolved experiments (mixing reactants and freezing at defined time points), 3D classification can capture the complete conformational trajectory of a molecular machine in action.

Practice Questions 3 questions

Prerequisite Chain

Understanding Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Dividing Integers → Unit Rates → Proportions → Percent Concept → Converting Between Fractions, Decimals, and Percents → Operations with Rational Numbers → Two-Step Equations → Solving Multi-Step Equations → Equations with Variables on Both Sides → Angle Pairs: Complementary, Supplementary, and Vertical → Parallel Lines and Transversals → Corresponding Angles → Alternate Interior Angles → Triangle Angle Sum Theorem → Exterior Angle Theorem → Triangle Inequality Theorem → Similar Triangles: AA Similarity → Similar Triangles: SSS and SAS Similarity → Proportions in Similar Triangles → Right Triangle Trigonometry Introduction → Sine, Cosine, and Tangent Ratios → Trigonometric Ratios Review → Radian Measure → Converting Between Degrees and Radians → The Unit Circle → Graphing Sine and Cosine → Graphing Tangent and Reciprocal Trigonometric Functions → Derivatives of Trigonometric Functions → Antiderivatives → Indefinite Integrals → Basic Integration Rules → Riemann Sums → Definite Integral Definition → Double Integrals: Definition and Setup → Iterated Integrals and Fubini's Theorem → Double Integrals over Rectangular Regions → Double Integrals over General Regions → Applications of Double Integrals: Area, Mass, and Moments → Triple Integrals in Cartesian Coordinates → Triple Integrals in Cylindrical and Spherical Coordinates → Change of Variables and the Jacobian Determinant → Applications of Triple Integrals: Volume and Mass → Vector Fields and Their Representations → Line Integrals of Vector Fields → Work and Circulation → Line Integrals of Scalar and Vector Functions → Fundamental Theorem for Line Integrals → Conservative Vector Fields → Conservative Vector Fields and Potential Functions → Curl and Divergence of Vector Fields → Curl and Divergence → Divergence Theorem → Electric Flux and Divergence Theorem → Gauss's Law: Integral Form and Meaning → Solving Problems with Gauss's Law → Conductors in Electrostatic Equilibrium → Capacitance and Capacitors → Dielectrics → Dielectric Constant and Relative Permittivity → Electric Field Inside Dielectric Materials → Dielectric Materials and Polarization → Dielectric Susceptibility and Permittivity → Energy Density in Electric Fields → Electric Current and Current Density → Electrical Resistance and Resistivity → Ohm's Law and Circuit Elements → Electromotive Force (EMF) and Batteries → Kirchhoff's Circuit Laws: Voltage and Current → DC Circuit Network Analysis Methods → Transient Response in RC Circuits → RC Circuits → LC and RLC Circuits → AC Circuits: Fundamentals → Impedance and Reactance → AC Power and Resonance → Electromagnetic Waves → Postulates of Special Relativity → Time Dilation → Length Contraction → Lorentz Transformation → Relativistic Velocity Addition → Relativistic Momentum and Energy → Mass-Energy Equivalence and E=mc² → Photons as Particles with Energy and Momentum → Planck-Einstein Relation: Energy and Frequency → Photoelectric Effect → The Photon: Light as Quanta → Compton Scattering → Wave-Particle Duality → de Broglie Wavelength → The Schrödinger Equation → State Vectors and Wavefunctions → Quantum Superposition → Quantum Entanglement → Bell Theorem and Bell Inequalities → Postulates of Quantum Mechanics → Observables and Quantum Operators → Commutators and Commutation Relations → Quantum Angular Momentum → Quantum Mechanical Treatment of Hydrogen → Solving the Schrödinger Equation for Hydrogen Atom → Quantum Numbers → Electron Configuration → Periodic Trends → Covalent Bonding → Electronegativity and Bond Polarity → Ionic Bonding → Lewis Structures → VSEPR Theory and Molecular Geometry → Molecular Geometry and Electron Pair Geometry → Molecular Polarity and Dipole Moments → Intermolecular Forces → States of Matter and Phase Changes: Melting, Boiling, and Sublimation → Gas Laws and the Ideal Gas Equation → Gas Stoichiometry and Volume-Volume Calculations → Thermochemistry and Enthalpy → Heat Capacity and Calorimetry → Entropy and Molecular Disorder → Spontaneity and ΔG → Entropy and Gibbs Free Energy → Chemical Equilibrium → Acid-Base Chemistry → Weak Acid Ionization → Weak Base Ionization → Acid and Base Strength: Ka, Kb, and Ionization → Leaving Groups and Nucleofugality → SN2 Substitution Reactions → SN1 Substitution Reactions → E1 Elimination Reactions → Alcohols and Ethers: Structure, Properties, and Nomenclature → Reactions of Alcohols → Aldehydes and Ketones: Structure and Reactivity → Oxidation Reactions in Organic Chemistry → Oxidation of Alcohols to Aldehydes and Ketones → Aldehyde and Ketone Structure and Nomenclature → Nucleophilic Addition to Aldehydes and Ketones → Carboxylic Acids and Their Derivatives → IUPAC Nomenclature of Carbonyls and Carboxylic Acids → IUPAC Nomenclature of Alkenes → Electrophilic Addition to Alkenes → Aromaticity and Benzene → Electrophilic Aromatic Substitution (EAS) → Nucleophilic Aromatic Substitution (SNAr) → Nucleophilic Acyl Substitution → Amines: Structure, Basicity, and Reactions → Amine Reactivity: Nucleophilicity and Basicity → Amino Acid Structure and Properties → Peptide Bonds and Polypeptide Formation → Protein Primary Structure → Protein Secondary Structure → Protein Tertiary Structure → Protein Denaturation and Renaturation → Protein Folding Pathways and Molecular Chaperones → Cryo-EM → Single-Particle Analysis

Longest path: 207 steps · 1063 total prerequisite topics

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